permut(m,n)=prod(i=0,n-1,m-i)
A094272(n,prev=0,debug=0,dontfactor=[])=
{
  /* Note: A094272(12) is best called as A094272(12,,,Set(8)) because A094272(11)-8 is hard to factor. */
  local(mult, result, p, q, x);
  if (!prev, prev = if(n>1, A094272(n-1,,debug), 0));
  mult = permut(prev, n-1);
  if (prev + n >= mult,
    result = prev + n;
    while (permut(result,n) % mult, result++);
  ,
    p = vecsort(concat(vector(n-1, i, if(!setsearch(dontfactor, i-1), factor(prev-i+1)[,1]~, []))));
    result = 0;
    for (c=1, #p,
      q = vector(c, i, p[#p-c+i]);
      if (q[1] == 1, next);
      if (debug, print1(c","));
      forvec (v=vector(c, i, [0, min(n, q[i])-1]),
        x = lift(chinese(vector(c, i, Mod(v[i], q[i]))));
        if ((!result | result>x) & (x>=prev+n) & (permut(x,n) % mult == 0),
          result = x;
        );
      );
      if (result, break);
    );
    if (debug, print);
  );
  result
}